So his current battery capacity is something like 17KW. Let's say that during the night would use 8 hours of battery time so the maximum a mining rig can use 2KW an hour. So for an S19 you'd need to under clock during the night to keep it running 24/7.

The main cost would be internet connection. Because of how remote he is, the only option for a constant internet connection is Starlink which has an initial cost of ~$700 and a monthly cost of $140. At current mempool fees he might be able to make enough sats to pay the monthly internet bill. Maybe if we start consistently seeing higher TX fees it could change. But the other metric that doesn't work in his favor is that hash rate continues to climb which makes his potential mining reward decline over time.